Abstract
Decomposition of tomographic reconstructions has many different practical application. We propose two new reconstruction methods that combines the task of tomographic reconstruction with object decomposition. We demonstrate these reconstruction methods in the context of decomposing directional objects into various directional components. Furthermore we propose a method for estimating the main direction in a directional object, directly from the measured computed tomography data. We demonstrate all the proposed methods on simulated and real samples to show their practical applicability. The numerical tests show that decomposition and reconstruction can combined to achieve a highly useful fibre-crack decomposition.
Highlights
X-ray Computed Tomography (CT) is a highly used non-invasive imaging technique
We propose a method for estimating the main direction in a directional object, directly from the measured computed tomography data
We have proposed two new tomographic reconstruction methods that makes utilize variational formulations
Summary
X-ray Computed Tomography (CT) is a highly used non-invasive imaging technique. Applications of this technique ranges from biological and chemical science, to structural and material science, where the resolution varies from large scale (meters) to micro-scale (nano-meters). In this paper the object is decomposed into a three components: the ground truth object, the limited data artifacts and the measurement noise, which are assumed to be sparse in the wavelet basis, the discrete cosine transform basis and in the sinogram domain, respectively. The other reconstruction method is motivated from the microlocal analysis results in [25], and utilizes regularization through a variational formulation to overcome consequential limited data artifacts We introduce both reconstruction methods in the light of reconstructing directional objects, and we demonstrate advantages and disadvantages of the reconstruction methods through empirical examples. Both sinogram splitting and DTVdecomposition makes use of the direction estimation method and DTV, but one method is obviously advantageous to the other and we introduce both method.
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